Question: Solve for $x$ and $y$ using substitution. ${6x+6y = 12}$ ${y = -2x+7}$
Since $y$ has already been solved for, substitute $-2x+7$ for $y$ in the first equation. ${6x + 6}{(-2x+7)}{= 12}$ Simplify and solve for $x$ $6x-12x + 42 = 12$ $-6x+42 = 12$ $-6x+42{-42} = 12{-42}$ $-6x = -30$ $\dfrac{-6x}{{-6}} = \dfrac{-30}{{-6}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {y = -2x+7}\thinspace$ to find $y$ ${y = -2}{(5)}{ + 7}$ $y = -10 + 7$ $y = -3$ You can also plug ${x = 5}$ into $\thinspace {6x+6y = 12}\thinspace$ and get the same answer for $y$ : ${6}{(5)}{ + 6y = 12}$ ${y = -3}$